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Math · Stage 5

Add and subtract fractions and mixed numbers (including unlike denominators)

When the bottoms are different, rename BOTH fractions to a common bottom (a shared multiple), then add or subtract the tops. For mixed numbers, work the wholes and the parts — regrouping one whole into extra parts when the top you are subtracting is too small.

✦ Math📘 Stage 5 · S5⏱ ~14 min🧒 Ages 9–10★ Free to start
I can add and subtract fractions and mixed numbers (including unlike denominators).
Start the free lesson →⬇ Printable PDF
Kavi the owl for Math
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Kavi's Two Brownie Trays 🍫

Kavi has 1/2 a tray of brownies 🍫, and a friend brings 1/3 of a tray. "I can't just add halves to thirds," hoots Kavi, "the pieces are different sizes!" So Kavi cuts both trays into sixths: now 1/2 = 3/6 and 1/3 = 2/6. "Same-size pieces at last — 3/6 + 2/6 = 5/6 of a tray!" Later Kavi joins two ribbons, 2 1/2 m and 1 1/3 m: "Add the wholes, add the parts — 3 5/6 m!"

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What your child will learn

1Different bottoms = different-size piecesHere is a whole cut into 2 equal parts with 1 shaded — that is 1/2. A third would cut the same whole into 3 parts instead. The pieces are not the same size, so you cannot add the tops yet. First you must make every piece the same size.
2Add unlike fractions: make the bottoms matchTo add 1/2 + 1/3, find a bottom both fit into — 6. Rename: 1/2 = 3/6 and 1/3 = 2/6. Now every piece is a sixth, so shade 5 of the 6 parts to show 3/6 + 2/6.
3Subtract unlike fractions the same wayTo work out 3/4 − 2/3, the smallest shared bottom is 12. Rename: 3/4 = 9/12 and 2/3 = 8/12. Now subtract the tops: 9/12 − 8/12. Shade just 1 of the 12 parts to show what is left.
4Two jobs, two rules
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A peek inside

Add 1/2 + 1/3.
a common bottom is 6: rename 1/2 = 3/6 and 1/3 = 2/6, then add the tops: 3/6 + 2/6

Try this at home: Rename both to sixths, then add: 1/2 + 1/3 = __

Ready to play and learn?

Start the free interactive lesson, or print the handout for screen-free play.

Start the free lesson →⬇ Download PDF

Part of Math · Stage 5 · S5 on KAVI Academy — a secular, whole-child learning platform for ages 5–12.